SMI 2012: Full Component-aware tensor-product trivariate splines of arbitrary topology

• Authors: Bo Li;Hong Qin
• Venue: Computers and Graphics
• Year: 2012

The fundamental goal of this paper aims to bridge the large gap between the shape versatility of arbitrary topology and the geometric modeling limitation of conventional tensor-product splines for solid representations. Its contribution lies at a novel shape modeling methodology based on tensor-product trivariate splines for solids with arbitrary topology. Our framework advocates a divide-and-conquer strategy. The model is first decomposed into a set of components as basic building blocks. Each component is naturally modeled as tensor-product trivariate splines with cubic basis functions while supporting local refinement. The key novelty is our powerful merging strategy that can glue tensor-product spline solids together subject to C^2 continuity. As a result, this new spline representation has many attractive advantages. At the theoretical level, the integration of the top-down topological decomposition and the bottom-up spline construction enables an elegant modeling approach for arbitrary high-genus solids. Each building block is a regular tensor-product spline, which is CAD-ready and facilitates GPU computing. In addition, our new spline merging method enforces the features of semi-standardness (i.e., @?"iw"iB"i(u,v,w)=1 everywhere) and boundary restriction (i.e., all blending functions are confined exactly within parametric domains) in favor of downstream CAE applications. At the computational level, our component-aware spline scheme supports meshless fitting which completely avoids tedious volumetric mapping and remeshing. This divide-and-conquer strategy reduces the time and space complexity drastically. We conduct extensive experiments to demonstrate its shape flexibility and versatility towards solid modeling with complicated geometries and non-trivial genus.